Rachel Counts (in more ways than one!)

I am enjoying Winter Break, a chance to catch my breath in the midst of a busy school year. We are in the Smokies with family for the holidays. This has given me lots of good time with granddaughter Rachel, who reports her age as three and three-quarters. Like her father and uncle when they were this age, she delights in patterns and numbers. We count pennies as we play dreidel. We count blocks and toys and the cookies we cut out of the sugar cookie dough. We count cards as we play Concentration (Memory), where she shows a strong visual memory. Her number sense seems to strengthen every day. We were building with her baby sister's blocks one day. We had established the previous day there were ten of the soft rubbery blocks in all. We were trying to recreate a structure we had built the day before, but could not as some were missing. She carefully counted out eight blocks. I asked her how many were missing. She thought for a moment. "Two! " she announced. Later we found one of the missing blocks and added a bear to the structure.

Who Knows How the Time Goes?

Telling Time is a usual topic for kids this age. Over the years, as digital clocks have become more common and analog clocks have become rarer, I've had to give thought to how much emphasis to put on telling time with an analog clock. While a digital clock is easier to "read," an analog clock, to my mind, gives a clearer sense of the passage of time and fractions of an hour. So while some of my students report that they do not have even one analog clock at home, I continue to spend some time on working with analog clocks. We use mini instructional clocks so that each student has one and can move the hands as we try to both set certain times and read times from the clock. I think one reason learning to read an analog clock is challenging for some students is that the numbers mean different things depending on whether you are looking at the hour hand or the minute hand. For concrete thinking seven and eight year olds, this can take some getting used to.

A Whole Lot of Counting Going On

And measuring and estimating and adding and multiplying and spotting shapes! On Thursday we had Math Day in Lower School. The morning was devoted to a variety of math activities. Each student got to choose 3 activities in which to participate, everything from Math Basketball and Math Baseball to Tangrams to Brain Teasers to Math Games. I offered a Math Scavenger Hunt. Students were challenged to count and measure various things on the playground and in the class. Some of the things they counted generated numbers to add and multiply. There were jars of items for estimation and counting. They looked for where they could find different geometric shapes on the playground and made a face with shapes. Fortunately the threatening clouds held off with their rain until afternoon, so students could measure the alligator sculpture in the Dragon Garden and do the other outside tasks. It was a great way to celebrate Math.

Turtle Explorations

We have been learning about a simple computer programming language called Logo that was developed at MIT as an educational aid for children. In Logo the cursor is a “turtle” who moves across the screen creating graphics based on the commands given by the children. We have learned some basic Logo commands, and students are beginning to write out programs (a series of commands) which they can then type into the computer to see the results. This project has generated a great deal of excitement in our group. It has also been our first time to use the new mobile laptop lab which has added to the excitement.

Real life math is not always neat and tidy

Today we did a journal problem that can sometimes trip up some of the students. Here is the problem:
Four friends found a bag with 18 marbles in it on the playground. They told Lisa, the Head Teacher, about it. She told them that if no one claimed the marbles in 2 weeks they could keep them. No one claimed the marbles. How can the friends share the marbles fairly? Use numbers, words, and/or pictures to explain your answer. Be sure you show what happens to all 18 marbles. Remember that in real world math, things do not always work out neatly and evenly.

One of the students called out after I read the problem, "Gee that's hard." One quickly wrote this solution: 18 (divided by) 6 = 3. When I asked him how that related to the numbers in the problem, he said, "Oops!" and went back to work. Things got pretty quiet as all the others settled down to work. Everyone was able to come up with a solution that accounted for all the marbles. Several suggested giving the extra two marbles to Lisa. One suggested giving them to two other friends. A couple needed a nudge to make their solutions clear. A lot of them used diagrams to show clearly their results. On Monday we will share solutions.

Countdown!

We usually begin math group with a whole group activity. After that we often work with partners or individually. Children often finish the work/project for the day at different times. If there is time left before snacktime at 10:00, they may have Math Choice. Choice time usually includes Job Cards (individual math task cards from Creative Publications and Marcy Cook), math workbooks, and math games from our math shelves. Currently the games on the shelf are Race for a Dollar and COUNTDOWN!.

COUNTDOWN! (by Cadaco) is a current favorite. In this game each player has wooden pegs numbered 1-10. In turn, players roll two dice. Each takes the two numbers generated and adds, subtracts, multiplies, or divides the two numbers. He/she turns over one peg representing the result of the operation chosen. For example, if 2 and 6 are rolled, the player can flip over 8 (2+6), 4 (6-2), or 3 (6 divided by 2). Multiplication does not work here as 2 X 6 is more than 10. The goal is to flip over all 10 number pegs. Some of the children are quicker at mental math and easily come up with the options. Others are helped by their fellow players to consider what numbers they can use. Over time they develop strategies, recognizing which numbers are harder to get and turning those over as soon as they can. It is a great game for strengthening students' understanding of number operations and their quick recall of math facts.

Challenge and Initiative

One of the problems in homework that was due on Friday asked the students "How big is your bike?" "Can you solve this problem?" The problem was from the Creative Publication's Primary Math Problems of the Day. There had been some earlier problems that provided enough information for students to solve the problem as well as some that did not. This was the first really open-ended problem in this area. Quite a few of the students found a way to solve this, measuring the length and/or height of their bikes using tools such as a ruler or a tape measure. One student reported that she did not have a bike. A few students had simply written "No" as an answer. When questioned, they said they did have bikes, but either they were not sure what to measure about the bike or were unsure what tool to use. "I know we have a tape measure somewhere, but I didn't know where it was." 

I used this as an opportunity to talk about "Initiative." I told my students that they are all smart (which is true!), but being smart only gets you so far. You also should take initiative and think creatively. I then asked the group to think about tools and materials we have used to measure things before, which include a variety of standard and non-standard measurement tools. I also asked what additional things we could use if we did not have a ruler or tape measure at home. Students came up with ideas using everything from string (you could cut a piece of string as long as your bike, then bring it to school to measure) to a crayon (see how many crayons long your bike is.) I then asked the bike owners who had not found a way to say how big their bikes were to take the sheet home and measure their bikes this weekend.